Chebyshev Expansion Of The Flow In A Spinning And Coning Cylinder

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Author Selmi, M. en_US
Available date 2009-11-25T13:03:18Z en_US
Publication Date 1994 en_US
Citation Engineering Journal of Qatar University, 1994, Vol. 7, Pages 151-170. en_US
URI http://hdl.handle.net/10576/7829 en_US
Abstract This paper is concerned with the calculation of the moments exerted by a viscous fluid on the walls of a cylinder that is spinning about its axis and coning about an axis that passes through its center of mass. For small coning angles and/or coning frequencies, these moments are estimated by solving the linearized Navier-Stokes equations. Solving the linearized Navier-Stokes equations is computationally expensive. Fortunately, when using the control volume approach to calculate these moments, these moments depend essentially on the axial velocity, and the linearized equations describing the deviation of the fluid motion from solid body rotation can be reduced to a single sixth-order partial differential equation governing the axial velocity. This single equation is solved by expanding the axial velocity in a triple series made of Fourier functions in the azimuthal direction and Chebyshev polynomials in the radial and axial directions. For linear analysis, only the fundamental component in the azimuthal direction is needed for the evaluation of moments and the triple series is reduced to a double Chebyshev expansion in the radial and axial directions thereby reducing the three-dimensional problem into a two-dimensional one. The results obtained by Chebyshev expansion show good agreement with those obtained by using eigenfunction expansion. en_US
Language en en_US
Publisher Qatar University en_US
Subject Engineering: Research & Technology en_US
Title Chebyshev Expansion Of The Flow In A Spinning And Coning Cylinder en_US
Type Article en_US
Pagination 151-170 en_US
Volume Number 7 en_US


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